Problem: At the school's carnival, one game featured this unique square dartboard with five smaller, shaded squares, shown here. The length of a side of the square dartboard is 4 times the length of a side of any of the five congruent, shaded squares. To win a prize, a player's dart has to land in a shaded region. If a player's dart randomly hits the dartboard, what is the probability of her winning a prize? Express your answer as a common fraction. [asy] size(100); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle); filldraw((0,0)--(1,0)--(1,1)--(0,1)--cycle, lightblue); filldraw((4,4)--(3,4)--(3,3)--(4,3)--cycle, lightblue); filldraw((3,0)--(4,0)--(4,1)--(3,1)--cycle, lightblue); filldraw((0,4)--(0,3)--(1,3)--(1,4)--cycle, lightblue); filldraw((1.5,1.5)--(1.5,2.5)--(2.5,2.5)--(2.5,1.5)--cycle, lightblue); [/asy]
Note that the entire square is equal to $4\times4=16$ of the smaller shaded squares. [asy] size(100); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle); filldraw((0,0)--(1,0)--(1,1)--(0,1)--cycle, lightblue); filldraw((4,4)--(3,4)--(3,3)--(4,3)--cycle, lightblue); filldraw((3,0)--(4,0)--(4,1)--(3,1)--cycle, lightblue); filldraw((0,4)--(0,3)--(1,3)--(1,4)--cycle, lightblue); filldraw((1.5,1.5)--(1.5,2.5)--(2.5,2.5)--(2.5,1.5)--cycle, lightblue); for(int i = 0; i <= 4; ++i) { draw((0,i)--(4,i)); draw((i,0)--(i,4)); } [/asy] Thus, the odds of a player's dart winning a prize is $\boxed{\frac{5}{16}}$.